#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dlagts_(integer *job, integer *n, doublereal *a, doublereal *b, doublereal *c__, doublereal *d__, integer *in, doublereal *y, doublereal *tol, integer *info) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DLAGTS may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)'*x = y, where T is an n by n tridiagonal matrix, for x, following the factorization of (T - lambda*I) as (T - lambda*I) = P*L*U , by routine DLAGTF. The choice of equation to be solved is controlled by the argument JOB, and in each case there is an option to perturb zero or very small diagonal elements of U, this option being intended for use in applications such as inverse iteration. Arguments ========= JOB (input) INTEGER Specifies the job to be performed by DLAGTS as follows: = 1: The equations (T - lambda*I)x = y are to be solved, but diagonal elements of U are not to be perturbed. = -1: The equations (T - lambda*I)x = y are to be solved and, if overflow would otherwise occur, the diagonal elements of U are to be perturbed. See argument TOL below. = 2: The equations (T - lambda*I)'x = y are to be solved, but diagonal elements of U are not to be perturbed. = -2: The equations (T - lambda*I)'x = y are to be solved and, if overflow would otherwise occur, the diagonal elements of U are to be perturbed. See argument TOL below. N (input) INTEGER The order of the matrix T. A (input) DOUBLE PRECISION array, dimension (N) On entry, A must contain the diagonal elements of U as returned from DLAGTF. B (input) DOUBLE PRECISION array, dimension (N-1) On entry, B must contain the first super-diagonal elements of U as returned from DLAGTF. C (input) DOUBLE PRECISION array, dimension (N-1) On entry, C must contain the sub-diagonal elements of L as returned from DLAGTF. D (input) DOUBLE PRECISION array, dimension (N-2) On entry, D must contain the second super-diagonal elements of U as returned from DLAGTF. IN (input) INTEGER array, dimension (N) On entry, IN must contain details of the matrix P as returned from DLAGTF. Y (input/output) DOUBLE PRECISION array, dimension (N) On entry, the right hand side vector y. On exit, Y is overwritten by the solution vector x. TOL (input/output) DOUBLE PRECISION On entry, with JOB .lt. 0, TOL should be the minimum perturbation to be made to very small diagonal elements of U. TOL should normally be chosen as about eps*norm(U), where eps is the relative machine precision, but if TOL is supplied as non-positive, then it is reset to eps*max( abs( u(i,j) ) ). If JOB .gt. 0 then TOL is not referenced. On exit, TOL is changed as described above, only if TOL is non-positive on entry. Otherwise TOL is unchanged. INFO (output) INTEGER = 0 : successful exit .lt. 0: if INFO = -i, the i-th argument had an illegal value .gt. 0: overflow would occur when computing the INFO(th) element of the solution vector x. This can only occur when JOB is supplied as positive and either means that a diagonal element of U is very small, or that the elements of the right-hand side vector y are very large. ===================================================================== Parameter adjustments */ /* System generated locals */ integer i__1; doublereal d__1, d__2, d__3, d__4, d__5; /* Builtin functions */ double d_sign(doublereal *, doublereal *); /* Local variables */ static integer k; static doublereal ak, eps, temp, pert, absak, sfmin; extern doublereal dlamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal bignum; --y; --in; --d__; --c__; --b; --a; /* Function Body */ *info = 0; if (abs(*job) > 2 || *job == 0) { *info = -1; } else if (*n < 0) { *info = -2; } if (*info != 0) { i__1 = -(*info); xerbla_("DLAGTS", &i__1); return 0; } if (*n == 0) { return 0; } eps = dlamch_("Epsilon"); sfmin = dlamch_("Safe minimum"); bignum = 1. / sfmin; if (*job < 0) { if (*tol <= 0.) { *tol = abs(a[1]); if (*n > 1) { /* Computing MAX */ d__1 = *tol, d__2 = abs(a[2]), d__1 = max(d__1,d__2), d__2 = abs(b[1]); *tol = max(d__1,d__2); } i__1 = *n; for (k = 3; k <= i__1; ++k) { /* Computing MAX */ d__4 = *tol, d__5 = (d__1 = a[k], abs(d__1)), d__4 = max(d__4, d__5), d__5 = (d__2 = b[k - 1], abs(d__2)), d__4 = max(d__4,d__5), d__5 = (d__3 = d__[k - 2], abs(d__3)); *tol = max(d__4,d__5); /* L10: */ } *tol *= eps; if (*tol == 0.) { *tol = eps; } } } if (abs(*job) == 1) { i__1 = *n; for (k = 2; k <= i__1; ++k) { if (in[k - 1] == 0) { y[k] -= c__[k - 1] * y[k - 1]; } else { temp = y[k - 1]; y[k - 1] = y[k]; y[k] = temp - c__[k - 1] * y[k]; } /* L20: */ } if (*job == 1) { for (k = *n; k >= 1; --k) { if (k <= *n - 2) { temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2]; } else if (k == *n - 1) { temp = y[k] - b[k] * y[k + 1]; } else { temp = y[k]; } ak = a[k]; absak = abs(ak); if (absak < 1.) { if (absak < sfmin) { if (absak == 0. || abs(temp) * sfmin > absak) { *info = k; return 0; } else { temp *= bignum; ak *= bignum; } } else if (abs(temp) > absak * bignum) { *info = k; return 0; } } y[k] = temp / ak; /* L30: */ } } else { for (k = *n; k >= 1; --k) { if (k <= *n - 2) { temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2]; } else if (k == *n - 1) { temp = y[k] - b[k] * y[k + 1]; } else { temp = y[k]; } ak = a[k]; pert = d_sign(tol, &ak); L40: absak = abs(ak); if (absak < 1.) { if (absak < sfmin) { if (absak == 0. || abs(temp) * sfmin > absak) { ak += pert; pert *= 2; goto L40; } else { temp *= bignum; ak *= bignum; } } else if (abs(temp) > absak * bignum) { ak += pert; pert *= 2; goto L40; } } y[k] = temp / ak; /* L50: */ } } } else { /* Come to here if JOB = 2 or -2 */ if (*job == 2) { i__1 = *n; for (k = 1; k <= i__1; ++k) { if (k >= 3) { temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2]; } else if (k == 2) { temp = y[k] - b[k - 1] * y[k - 1]; } else { temp = y[k]; } ak = a[k]; absak = abs(ak); if (absak < 1.) { if (absak < sfmin) { if (absak == 0. || abs(temp) * sfmin > absak) { *info = k; return 0; } else { temp *= bignum; ak *= bignum; } } else if (abs(temp) > absak * bignum) { *info = k; return 0; } } y[k] = temp / ak; /* L60: */ } } else { i__1 = *n; for (k = 1; k <= i__1; ++k) { if (k >= 3) { temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2]; } else if (k == 2) { temp = y[k] - b[k - 1] * y[k - 1]; } else { temp = y[k]; } ak = a[k]; pert = d_sign(tol, &ak); L70: absak = abs(ak); if (absak < 1.) { if (absak < sfmin) { if (absak == 0. || abs(temp) * sfmin > absak) { ak += pert; pert *= 2; goto L70; } else { temp *= bignum; ak *= bignum; } } else if (abs(temp) > absak * bignum) { ak += pert; pert *= 2; goto L70; } } y[k] = temp / ak; /* L80: */ } } for (k = *n; k >= 2; --k) { if (in[k - 1] == 0) { y[k - 1] -= c__[k - 1] * y[k]; } else { temp = y[k - 1]; y[k - 1] = y[k]; y[k] = temp - c__[k - 1] * y[k]; } /* L90: */ } } /* End of DLAGTS */ return 0; } /* dlagts_ */